According to PWInsider.Com, the Dudley Boyz will still be allowed to use their "family name" even when wrestling elsewhere. Apparently, when the Dudleys signed with WWE, Paul Heyman struck a deal where Bubba Ray and D-Von would still be allowed to use their name when their tenure with the company ended.

Thus, Bubba Ray and D-Von will be able to wrestle as the Dudley Boyz wherever they end up wrestling in the future.

News courtesy of PWInsider.Com:

"A few readers have wondered which, if any, released WWE workers will be able to keep their ring names once they begin working for other organizations. Well, in the case of the Dudley Boyz, Bubba and D-Von will retain the names they are known by once their deals with WWE have expired. As I discussed in an Elite Audio report yesterday, back in 1999, when the Dudleys left ECW for the then-WWF, ECW owned the copyrights and trademarks on the Dudleys name. ECW and Paul Heyman signed over the rights to the name, and to repay the Dudleys for all they did for ECW, it was arranged where the rights would revert back to Bubba & D-Von after the license with WWE expired. So, the Dudley Boyz will be able to use the Dudleys name wherever they go."